Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}4x+6y &= 3 \\ -2x+2y &= 4\end{align*}$
Solution: Begin by moving the $x$ -term in the second equation to the right side of the equation. $2y = 2x+4$ Divide both sides by $2$ to isolate $y$ $y = {x + 2}$ Substitute this expression for $y$ in the first equation. $4x+6({x + 2}) = 3$ $4x + 6x + 12 = 3$ Simplify by combining terms, then solve for $x$ $10x + 12 = 3$ $10x = -9$ $x = -\dfrac{9}{10}$ Substitute $-\dfrac{9}{10}$ for $x$ back into the top equation. $4( -\dfrac{9}{10})+6y = 3$ $-\dfrac{18}{5}+6y = 3$ $6y = \dfrac{33}{5}$ $y = \dfrac{11}{10}$ The solution is $\enspace x = -\dfrac{9}{10}, \enspace y = \dfrac{11}{10}$.